The number of number-pairs lying between 40 and 100 with their H.C.F as 15 is:
A 3
B 4
C 5
D 6
E 7
A 3
B 4
C 5
D 6
E 7
First of all, the GMAT will not expect test-takers to know what HCF stands for.
There's also some ambiguity about whether the number pair (45, 60) is different from (60, 45)
Here's how I would have written the question...
If 15 is the greatest common divisor of x and y, then 15 must be a divisor of x and yHow many unique pairs of integers (x, y) exist such that 40 < x < y < 100, and the greatest common divisor of x and y is 15?
A 3
B 4
C 5
D 6
E 7
Or we can say that x and y must be multiples of 15
There are only four multiples of 15 in the given range: 45, 60, 75, 90
Since the answer choices range from 3 to 7, let's just LIST the possible pairs where the greatest common divisor is 15
(45, 60)
(45, 75)
(60, 75)
(75, 90)
There are 4 such pairs
Answer: B
Cheers,
Brent
